The Dicke model of superradiance studied in a previous paper by Wang and Hioe is generalized (i) to include an interaction energy of the form ${a}^{\ifmmode\dagger\else\textdagger\fi{}}{\ensuremath{\sigma}}^{+}+a{\ensuremath{\sigma}}^{\ensuremath{-}}$, where $a,{a}^{\ifmmode\dagger\else\textdagger\fi{}}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}},{\ensuremath{\sigma}}^{+}$ are the usual photon and spin operators, (ii) to include the spatial variation of the electromagnetic field, and (iii) to include the possibility of small classical motions of atoms from their equilibrium positions. The free energies of these generalized models are calculated exactly in the thermodynamic limit, and their phase-transition properties are presented.The Dicke model of superradiance studied in a previous paper by Wang and Hioe is generalized (i) to include an interaction energy of the form ${a}^{\ifmmode\dagger\else\textdagger\fi{}}{\ensuremath{\sigma}}^{+}+a{\ensuremath{\sigma}}^{\ensuremath{-}}$, where $a,{a}^{\ifmmode\dagger\else\textdagger\fi{}}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}},{\ensuremath{\sigma}}^{+}$ are the usual photon and spin operators, (ii) to include the spatial variation of the electromagnetic field, and (iii) to include the possibility of small classical motions of atoms from their equilibrium positions. The free energies of these generalized models are calculated exactly in the thermodynamic limit, and their phase-transition properties are presented.

Physical Review ASep 1, 1973165 citations

Superradiant switching, quantum hysteresis, and oscillations in a generalized Dicke model

Kevin C. Stitely, Stuart J. Masson, Andrus Giraldo +2 more

We demonstrate quantum signatures of deterministic nonlinear dynamics in the transition to superradiance of a generalized open Dicke model with different coupling strengths for the co- and counterrotating light-matter interaction terms. A first-order phase transition to coexisting normal and superradiant phases is observed, corresponding with the emergence of switching dynamics between these two phases, driven by quantum fluctuations. We show that this phase coexistence gives rise to a hysteresis loop also for the quantum mechanical system. Additionally, a transition to a superradiant oscillatory phase is observed clearly in quantum simulations.We demonstrate quantum signatures of deterministic nonlinear dynamics in the transition to superradiance of a generalized open Dicke model with different coupling strengths for the co- and counterrotating light-matter interaction terms. A first-order phase transition to coexisting normal and superradiant phases is observed, corresponding with the emergence of switching dynamics between these two phases, driven by quantum fluctuations. We show that this phase coexistence gives rise to a hysteresis loop also for the quantum mechanical system. Additionally, a transition to a superradiant oscillatory phase is observed clearly in quantum simulations.

arXiv:2007.13271Physical Review ADec 2, 202033 citations

Superradiance in the Dicke Model

E.P. Kadantseva, W. Chmielowski, A.S. Shumovsky

Springer series on wave phenomenaJan 1, 19900 citations

Phase Transition in the Dicke Model of Superradiance

Y. K. Wang, F. T. Hioe

A system of $N$ two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied. By making use of a set of Glauber's coherent states for the field, the free energy of the system is calculated exactly in the thermodynamic limit. The results agree precisely with those obtained by Hepp and Lieb, who studied the same model using a different method. The exhibition of a phase transition of the system is presented mathematically in an elementary manner in our approach. The generalization to the case of finitely many radiation modes is also presented.A system of $N$ two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied. By making use of a set of Glauber's coherent states for the field, the free energy of the system is calculated exactly in the thermodynamic limit. The results agree precisely with those obtained by Hepp and Lieb, who studied the same model using a different method. The exhibition of a phase transition of the system is presented mathematically in an elementary manner in our approach. The generalization to the case of finitely many radiation modes is also presented.

Physical Review AMar 1, 1973745 citations

Superradiance and subradiance on theedge of Dicke’s regime

Igor Ferrier-Barbut

Sep 1, 20210 citations

A system of

N

two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied. By making use of a set of Glauber's coherent states for the field, the free energy of the system is calculated exactly in the thermodynamic limit. The results agree precisely with those obtained by Hepp and Lieb, who studied the same model using a different method. The exhibition of a phase transition of the system is presented mathematically in an elementary manner in our approach. The generalization to the case of finitely many radiation modes is also presented.